GLOBAL DYNAMICS OF A TIME-DELAYED ZIKA VIRUS MODEL WITH INCUBATION PERIOD

Abstract

Zika virus (ZIKV), primarily transmitted by <i>Aedes</i> mosquitoes, can cause severe neurological complications and has triggered multiple outbreaks worldwide in recent years. In this paper, we develop a time-delayed transmission model incorporating the human incubation period and an exposed host compartment. The basic reproduction number $ R_0 $ is derived, and the local asymptotic stability of both the disease-free and endemic equilibria is established. By constructing suitable Lyapunov functionals, the global asymptotic stability of both equilibria is further demonstrated. Numerical simulations further illustrate the theoretical results, showing that the disease dies out when $ R_0 &lt; 1 $ and persists when $ R_0 &gt; 1 $. Furthermore, an optimal control framework involving five intervention measures is formulated and analyzed. Numerical results show that the proposed control strategies effectively reduce disease transmission, with vaccination and treatment exhibiting the greatest impact among the considered interventions. In addition, sensitivity analysis reveals the relative influence of model parameters on $ R_0 $. Overall, this model enhances our understanding of ZIKV transmission dynamics and provides theoretical support for the design of effective control strategies.